One‑Way ANOVA

One‑Way ANOVA (Analysis of Variance) is a powerful tool for comparing the means of three or more groups. Instead of running multiple t‑tests—which increases the risk of Type I error—ANOVA evaluates all groups simultaneously. This makes it ideal for comparing machines, shifts, suppliers, product types, or any other categorical factor with multiple levels. 

ANOVA works by partitioning total variation into variation between groups and variation within groups. If the between‑group variation is significantly larger than the within‑group variation, it suggests that at least one group differs from the others. 

The test produces an F‑statistic and a p‑value. A significant result indicates that differences exist, but it does not specify which groups differ. Post‑hoc tests, such as Tukey’s method, help identify specific pairwise differences. 

ANOVA assumes normality, independence, and equal variances. When these assumptions are violated, transformations or non‑parametric alternatives may be appropriate. 

In the Analyze phase, ANOVA helps you identify which factors contribute to variation and where improvement efforts should focus. It provides a structured, statistically sound way to compare multiple groups and uncover meaningful differences in process performance.